Overview

The average mathematical competence of U.S.
students lags far behind that of peers in East Asia and much of Europe. Few U.S. students possess the knowledge
of mathematics needed to pursue careers in STEM disciplines. Many lack even the
basic competence needed to succeed in most jobs in a modern economy. Moreover, a large gap separates the
mathematical knowledge of children from rich and poor backgrounds and from
differing racial and ethnic groups; differences are already present in
preschool and increase over the course of schooling. The goal of the Center for Improving Learning of Fractions (CILF) is
to apply theories, methods, and empirical findings from cognitive science
research on the acquisition of mathematical knowledge to better understand the problems
that children with mathematics difficulties (MD) have with a crucial component
of mathematical knowledge – rational numbers – and to develop effective
interventions to remedy those problems.

The Center research program comprises three strands.
In Strand 1, we are conducting relatively small-scale experimental studies to enhance
understanding of the cognitive processes that underlie magnitude representations of rational
numbers and use of those representations in operations with rational numbers. In Strand 2, we are conducting short-
and long-term longitudinal studies of students with and without MD to examine
how numerical magnitude representations, proficiency with whole number
operations, working memory for numbers, inhibitory processes, attentive
behavior, and strategic behavior contribute to the ability to understand and
operate with rational numbers. As results from research conducted within Strands
1 and 2 emerge, they are informing the design of the instructional innovations,
which are the focus of Strand 3. In Strand 3, our major focus is on building a
solid foundation of conceptual understanding of fractional magnitudes by
working on concepts and procedures involved in common fractions and decimal equivalents.
Each year in Years 1-5, we develop an intervention component, integrate it into
the overall intervention package, and conduct research to develop an
evidence-based fidelity of implementation tool and assess its feasibility. This
also provides us with data for estimating the effects of each year’s component
on conceptual understanding and procedural skill with fractional quantities and
for assessing whether effects differ as a function of MD severity; these data
are used to inform the next year’s development work.